At least 34 people, including 15 babies and children, drowned when their overcrowded boat capsized in high winds off a Greek island on Sunday, the latest migrant tragedy at sea.

The new deaths came as Athens angrily defended its handling of the mounting refugee crisis in Europe and appealed for more help.

Four babies and 11 young children -- six boys and five girls -- were among those on the stricken wooden boat when it sank off the island of Farmakonisi.

Eight of the victims were found by coastguard frogmen in the hold of the boat.

A total of 34 people were found dead, while another 68 were plucked alive from the sea and a further 30 managed to swim to safety on a beach on the island, according to latest coastguard figures.

The exact number of those aboard remains unknown but the ANA said the boat was overcrowded and went down because of high winds in the area.

A Greek navy ship was taking the bodies to Rhodes while the survivors were being transported to Leros.

The coastguard was also still searching on Sunday for four children missing after another boat capsized on Saturday off Samos, a Greek island just off the Turkish coast.

The latest tragedies follow the death of a Syrian toddler whose lifeless body was photographed washed up on a Turkish beach last week, becoming a heartwrenching symbol of the plight of refugees fleeing war.

The International Organisation for Migration has said more than 430,000 migrants and refugees had crossed the Mediterranean to Europe so far in 2015, with 2,748 dying or going missing en route.

- 'We must mourn but also act' -

Interim Prime Minister Vassiliki Thanou on Sunday branded criticism of Greece, which has been on the frontline of the surge of migrants trying to reach Europe, as "unacceptable".

"Greece is strictly applying European and international treaties without ignoring the humanity of the situation," she said on a visit to Lesbos, an island which has been struggling with the massive influx.

German Chancellor Angela Merkel on Saturday called on Athens, already grappling with a deep economic crisis, to make more effort to protect the EU's external borders.

"We have a second external border, that's between Greece and Turkey, where we need protection. And this protection is at the moment not being guaranteed," she said.

"Greece needs to take its responsibility... we will also speak with Turkey."

But Greece's leftist Syriza party, bidding for reelection in next Sunday's vote, called for external help in dealing with the crisis.

"We should mourn but also act," it said in a statement, describing the massive influx of refugees as a wider European and global problem.

"Our country is, because of its geographic position, a gateway and it needs support, funds and infrastructure in order to help these desperate people, as it must do."

Marine Minister Christos Zois also issued a statement to highlight the "daily superhuman struggle" of the Greek costguard to "save thousands of people, victims of human smugglers".